Archive for June, 2010

Hey everyone! I am at the ISTE’s annual conference in Denver, Colorado (International Society for Technology in Education). I went to some great sessions today. Three important websites I’d like to share:

1. Brainpop – I went to a research session on the effectiveness of Brainpop in improving students’ academic achievement. The research looks promising and shows statistically significant achievement in the students that used Brainpop as a supplement to their learning. I have seen the math Brainpop videos used effectively in some classrooms. The videos are engaging, filled with rich content and student centered. Some of it is free. For most of it, you have to have a subscription. It helps make math content more accessible through funny cartoons about various math topics. http://www.brainpop.com/ and http://www.brainpop.com/free_stuff/ and http://www.brainpopjr.com/

3. Create a Graph -This is a site by the National Center for Education Statistics (http://nces.ed.gov/nceskids/createagraph/). It is a website to help children understand, read and create different types of graphs and charts.

What are your dominant intelligences? Do you know? Because you teach from them. We all teach from our strengths and yet we have students who learn from the spaces where we aren’t so dominant. Here is a great site to test your intelligences (be sure to take the free test):

We have to make sure we have a full toolkit so we can reach all of our students. Howard Gardner built upon several theories to formalize and popularize this idea of multiple intelligences -the idea that students learn in 9 different ways. This theory directly impacts our guided math groups because the way we shape lessons should springboard from these ways. We try different approaches with different students. When we teach from the space they learn, they get it. In the next few posts I will discuss each one of the intelligences and how to build on them during guided math lessons.

Papert (1996) tells the story of an exchange between two kindergarteners while exiting the computer lab. One student was exiting with their class and the other was entering.

“[Upon exiting the child waiting to enter asked] “What was it like?” The friend replied, “It was fun.” Then paused and added: “It was really hard.” The relation between “fun” and “hard” may need some interpretation. Did this mean “it was fun in spite of being hard” or “it was fun because it was hard”? The teacher who heard the tone of the conversation and knew the children had no doubt. The child meant it was “fun” because it was “hard.” Since then I have listened to children with an ear sensitized by this experience and have come to know that the concept of hard fun is widely present in children’s thinking (Cited in Andrews & Trafton, 2002).”

This passage provokes me to think about the type of “hard fun” which we engage children in during math class. Hard fun is academically rigorous tasks that engage the whole child. When students are having “hard fun” both their hands and their minds are engaged. When students are having “hard fun” they are doing rich mathematical tasks that push them to reach and learn. When students are having “hard fun” they laugh, they communicate and they struggle through the difficult parts hanging onto all the scaffolds we set up.

Today, I interviewed several upper elementary students about math. These were students who had failed the math test and were going to be going to summer school. I wanted to know what their perception of what happened was. Surprisingly, they all said they liked math and felt they had a handle on it. I thought, “Wow!” What does this mean? So, I told them that I would like to do a “math interview” with them, where we would discuss problems and how they solved them. They agreed and we were off!

Now there are several types of interviews, but I did a content interview. I wanted to know what they knew. This experience just reminds me again, that IT’S really important that we talk to students about math. Some things we will only ever know by having a conversation. We should be doing math conferences. We have to find time in our schedules. Even if we only do 1 or 2 a semester, it is probably more than we have been doing. Math conferences can make all the difference in a student’s progress. When student’s have the time to talk about math and their individual performance, they have the opportunity to set goals. When students set goals, they have the opportunity to meet them. So, look at the forms I’ve uploaded and use them! And let me know how they work, please:)

meaning = (1) to grow vigorously (2) to progress toward or realize a goal despite or because of circumstances (Merriam-Webster,2010)

Guided math provides students an opportunity to thrive, to grow vigorously toward their mathematical goals (despite their particular circumstances and because of the particularized learning structure). A small group setting allows teachers to go deep…to really get at the misconceptions, misunderstandings and error patterns. It allows students to engage in mathematical conversations that illuminate their thinking outloud. This type of public thinking in a small group helps students to grow as mathematicians. They can ask questions, take risks, talk about difficulties in ways that they aren’t comfortable doing and often are impossible in a whole group setting. Guided math provides a space to gain conceptual understanding through hands-on activities and pictorial representations. It provides a space to practice procedural fluency, make mistakes and talk about them. It provides space to engage in intense problem solving outloud, with partners, in a small guided group so the teacher can scaffold the thinking. In small guided math groups students become thrivers. Thrivers are thriven. Thriving builds confidence. And most importantly, students who have thriven in small groups are more likely to go back to centers and independent work believing in themselves and their mathematical skills.

I was inspired by a blogpost that talked about the traditional game of war being worth a 1000 worksheets. Visit this post on that site!(http://letsplaymath.net/2006/12/29/the-game-that-is-worth-1000-worksheets/). This idea totally resonated with me because I believe that not only the game of war, but various games that we play in the classroom can help students get excited about learning and want to stay engaged in purposeful practice for long periods of time. I think that cards, dice and dominos are the keys to the mathematical practice kingdom. Spinners are also great. All of these number generators give students the base of what they need to explore the basic arithmetic facts. Gameboards also can provide another space for active engagement.

Gameboards can provide a great space for engaging students in academically rigorous thinking tasks. They also have the added bonus of building social skills and character. A growing body of research suggests that games can and do improve math skills (see http://www.edweek.org/ew/articles/2008/04/30/35games_ep.h27.html),

I can set out 5 teacher made educational game boards and tell students to do totally different things. For example:

Group 1: Play doubles- Roll the dice, double the number and move that many spaces. Whoever reaches the finish line first wins.

Group 2: Play +10 ( they can use the number line as a scaffold)- Roll the dice, add ten and move that many spaces. Whoever reaches the finish line first wins.

Group 3: Play Lucky 8 (a game to practice compensation) – Pull a card, add eight to that number and move that many spaces. Whoever reaches the finish line first wins.

Group 4: Play Lucky 9 (a game to practice compensation) – Pull a card, add nine to that number and move that many spaces. Whoever reaches the finish line first wins.

Group 5: Roll 3 and Add. Eachg player generates 3 different numbers, adds them together and moves that many. Whoever reaches the finish line first, wins.

Think: “How can I make this standard into a boardgame?” What exactly do I want them to practice? Where’s the math?

Buy lots of different game boards and adopt them. The game should be fun and have an element of strategy and chance. Throw in a few “Pass Go,” “Lucky Break” or “2 extra point” roadblocks.

Include artifacts where they have to record/show their thinking along the way. At the very least have a summary sheet where they can do some sort of brief reflection at the end.

Be sure to differentiate the games by readiness levels. Everybody should get an opportunity to play, but usually I would make sure students are practicing in their “zone of proximal development “-somewhere where they are building their skill sets.

Give it a Professional Look – Students don’t want to play anything that looks raggedy. Be proud of your gameboards.

Develop a Good Set of Rules – Make sure everybody understands them. Have several sets so students can refer to them during the game. Make sure they know how to set up, play, and win the game.

Bonus Tip: Have your students create some of the gameboards! They have to pick a topic they are struggling with and then make a game for them to practice and get better at that skill.

As quiet as it’s kept, there are theories about teaching math. People research it. They develop theories about it. One of the best kept secrets is that Math has Dolch Words (Newton, 2008). In Language arts we talk about the necessity that students know their dolch words- words that they must know in order to read fluently. Same with math. Van De Walle (http://www.ablongman.com/vandewalleseries/) has outlined some of these “words.” Our children need to know the basic facts (there are 100 addition and 100 subtraction ones) like the back of their hand. Basic facts are all the facts from 0 through 18. There is a way to teach them (according to math theory). In our guided math groups, different groups of students will be working on different types of facts. Just as in reading, everybody isn’t studying the same words. Some kids know all the words from list 1, they might be on list 5. Same with math.

We want our students to understand what addition and subtraction means (to have conceptual understanding). It is just as important that they have procedural fluency (automaticity and fluency) as well as problem solving skills. The “dolch words” gives teachers a frame to ensure that students learn all the facts so they are fluent by the time they start multiplying and dividing. The upper elementary students have trouble with math because they don’t know their basic addition and subtraction “dolch words.” Here’s a list of the most common “math dolch words”- facts students should know so they do math with automaticity:

+0 facts

+1 facts

+2 Facts

complements of 5

complements of 10

doubles

doubles +1

doubles +2

lucky 7

lucky 8 facts

lucky 9 facts

-0 facts

-1 facts

easy subtraction facts using known facts

harder subtraction facts – adding up to subtract

What do you do in your classroom to track student’s progress with the “dolch words” of math? Do your student’s have any concept of what they have learned and what they still need to study? In what ways do you think some sort of individualized tracking system might help them in learning their basic facts?

Balanced Assessment is one of the linchpins of great math instruction. It is an integral part of planning for guided math groups. Balanced Assessment is premised on the McTighe and Wiggins (2004) idea that assessment should be a scrapbook rather than a snapshot. We should have multiple pictures of what students can do by giving them ample opportunity to demonstrate their knowledge in a variety of ways. We should begin each unit of study by pre-assesing our students. This can be done through a variety of pre-assessments such as surveys, questionnaires, checklists and quizzes. Moreover, teachers should be strategically using ongoing assessments such as anecdotals, math inventories, exit slips for lessons and conferences. Finally, teachers should use a variety of summative assessments such as project menus, short essays and chapter tests with both multiple choice and constructed response questions. If we are really going to use assessement as a powerful way to move our instruction and advance student achievement, then we must move beyond teach, test and move on.

How are you using balanced math components in your classroom? Please leave comments and questions:)

There are some really great virtual manipulative sites out there! Remember we are teaching “digital natives.” Here are 3 ways to maximize use of them in your classroom.

1. Use them for guided math lessons. Move your group to the computers and do work with them using these sites.

2. Use them as a whole group mini lesson. Pull these lessons up on an lcd or smart board, they add a great dimension to the lesson. If you don’t have these options, go and teach a lesson to your class in the computer lab. It is worth it!

3. Set them up as one of the math center stations. It is very important that you have specific activities for the students to do. These can be powerfully potential, scaffolded, interactive learning spaces that provide immediate feedback.

4. Who out there is presently using virtual manipulatives in their classroom? What are your experiences? Please share ideas and issues:)

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